You have been asked to estimate the value of Cavanaugh Motels, a motel chain. The firm reported earnings of \($200\) million before interest and taxes in the most recent year and paid 40% of its taxable income in taxes. The book value of capital at the firm is \($1.2\) billion, and the firm expects to grow 4% a year in perpetuity. The firm has a beta of 1.2, a pretax cost of debt of 6%, equity with a market value of \($1\) billion, and debt with a market value of \($500\) million. (The risk-free rate is 5%, and the market risk premium is 5.5%.)

a. Estimate the value of the firm, using the cost of capital approach.

b. If you were told the probability of default at this firm at its current debt level is 10% and that the cost of bankruptcy is 25% of unlevered firm value, estimate the value of the firm using the adjusted present value approach.

c. How would you reconcile the two estimates of value?